Some anisotropic universes in the presence of imperfect fluid coupling with spatial curvature

TL;DR

This paper explores anisotropic Bianchi universes with imperfect fluids, deriving exact solutions and analyzing conditions under which these models approach isotropy, highlighting that near-isotropy of the universe does not imply isotropic fluid properties.

Contribution

It introduces a novel coupling of the energy-momentum tensor with spatial curvature to obtain exact anisotropic universe solutions and examines their isotropization behavior.

Findings

Exact solutions for anisotropic universes with constant deceleration

Models can approach isotropy despite anisotropic fluids

Impossibility of inferring fluid isotropy from universe isotropy

Abstract

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI0-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinetly expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.